Simplify the following expression: $q = \dfrac{k^2 - 8k + 7}{k - 1} $
First factor the polynomial in the numerator. $ k^2 - 8k + 7 = (k - 1)(k - 7) $ So we can rewrite the expression as: $q = \dfrac{(k - 1)(k - 7)}{k - 1} $ We can divide the numerator and denominator by $(k - 1)$ on condition that $k \neq 1$ Therefore $q = k - 7; k \neq 1$